Consider a metal sphere of radius r, drag coefficient C, density p_s falling in a fluid p and viscosity n.
Find the acceleration:
I found this to be g - p/p_s * g - (3C/(8*p_s*r))*v^2. Others were in agreeal with this so take it as given.
***Show that your result has the solution v=atanh(bt) and find constants a and b.***
***the part im on
(read other parts)
The Attempt at a Solution
So, I let C = g-p/p_s* g since this is a constant term and the same for the ones preceding v^2. I just let P = this stuff.
Thus i have v'=C-P*v^2
Now I have no idea how to solve this DE with the knowledge that I have but the general form of the solution was given.
So I'm guessing there's some sort of other way to verify it, but I'm not sure how.
PS: I'm assuming an initial condition is v(0) = 0 as this was needed in another part.